Limit Cycles Bifurcating from a Class of Cubic Hamiltonian Systems

Abstract

In this paper, the perturbation of a class of cubic Hamiltonian systems is considered. Using Abelian integral, we prove that there exists a neighborhood of the center where the system has at most two limit cycles for arbitrary polynomial perturbation of degree three or four, and at most four limit cycles for arbitrary polynomial perturbation of degree five or six, respectively, which can be reached.